What policy objective should a common central bank in a heterogeneous monetary union pursue? Should it base its decisions on the EU-wide average of inflation and growth or should it instead focus on (appropriately weighted) national rates of inflation and growth? We find that a central bank that minimises the national welfare losses reacts less to common shocks. However, average union-wide expected welfare is lower under a central bank that cares about union-wide variables if the variability of common shocks is large relative to the inflation bias. For a single country, welfare is lower in this case if its transmission mechanism is close to the average. The inflationary bias depends on the interaction between the transmission mechanism and distortions in labour markets.